Hamiltonian systems with continuous spectrum and vortex structures in rotating fluid

The problem of small oscillations of rotating inviscid incompressible fluid is considered. The linearization of the Euler equation in the rotating coordinate system on the solution, which corresponds to the rotation of the fluid as a rigid body around z–axis, gives the system of differential equations, first obtained by H. Poincaré.The systematic investigation of the systems of equations of this new type began with the work of S.L. Sobolev.